Temperature-Dependent Kinetic Study of the Reactions of Hydrogen Atoms with H₂S and C₂H₄S

Abstract

A discharge-flow reactor combined with modulated molecular beam mass spectrometry technique was employed to determine the rate constants of H-atom reactions with hydrogen sulfide and thiirane. The rate constants for both reactions were determined at a total pressure of 2 Torr from 220 to 950 K under pseudo-first-order conditions by monitoring either consumption of H atoms in excess of H₂S (C₄H₄S) or the molecular species in excess of atomic hydrogen. For H + H₂S reaction, a suggested previously strong curvature of the Arrhenius plot was confirmed: k_l = 8.7 × 10⁻¹³ × (T/298)^2.87 × exp(−125/T) cm³ molecule⁻¹ s⁻¹ with a conservative uncertainty of 15% at all temperatures. Non-Arrhenius behavior was also observed for the reaction of H-atom with C₂H₄S, with the experimental rate constant data being best fitted to a sum of two exponential functions: k₂ = 1.85 × 10⁻¹⁰ exp(−1410/T) + 4.17 × 10⁻¹² exp(−242/T) cm³ molecule⁻¹ s⁻¹ with an independent of temperature uncertainty of 15%.

1. Introduction

The present work reports temperature-dependent measurements of rate constants for two elementary reactions involving hydrogen atoms, with H₂S and C₂H₄S. The H-atom reaction with H₂S is of importance in combustion chemistry and industrial processes, and is included in a detailed chemical mechanism to describe reactions in the H₂–S₂–H₂S system [1]:

H + H₂S → SH + H₂

(1)

The temperature dependence of the rate constant of reaction (1), which proceeds through the abstraction of a hydrogen atom, is also of theoretical interest, in particular for assessing the effect of quantum tunneling [2,3]. Reaction (1) has been intensively studied over the past few decades, both experimentally [4,5,6,7,8,9,10,11,12,13,14,15] and theoretically [2,3,13,15,16]. Although there is now some experimental and theoretical evidence for the curvature of the Arrhenius plot for reaction (1), it has never actually been observed experimentally in any single study conducted over a sufficiently wide temperature range. All previous experimental work was carried out over a limited temperature range, and “unmodified” Arrhenius expressions were reported for the reaction rate constant. One of the aims of this work was to provide experimental evidence of the curvature of the Arrhenius dependence of k₁ within the framework of one study through rate constant measurements over an extended temperature range, T = 220–950 K.

It is known that reactions of C₂H₄S (thiirane, ethylene sulfide) with various atoms are rapid and proceed through S-atom abstraction, leading to almost stoichiometric production of ethylene and sulfur-containing radicals [17,18,19,20]. This allows the desulfurization reactions of thiirane to be used in laboratory research both as sources of radicals and as scavengers of unwanted active species. The reaction of C₂H₄S with hydrogen atoms leads to the formation of SH (an important intermediate in atmospheric and combustion chemistry [21,22]), and can be used as an alternative source of SH radicals to those involving H₂S [23].

H + C₂H₄S → SH + C₂H₄

(2)

The kinetic information on reaction (2) is rather scarce and uncertain. Only two measurements of the reaction rate constant were reported, by Yokota et al. [24] at T = 300–425 K using the relative rate method, and in absolute measurements by Lee et al. from 223 to 423 K [20]. The activation energies reported in two studies are very close; however, the absolute values of the reaction rate constant differ by a factor of 3. The objective of the present work was to provide new measurements of the rate constant over an extended temperature range, T = 220–950 K.

2. Results and Discussion

2.1. Reaction H + H₂S

2.1.1. Measurements of the Reaction Rate Constant

All measurements were carried out under flow conditions at nearly 2 Torr of total pressure of Helium, and with detection of the gas phase species involved using mass spectrometry [23].

The reaction rate constant was determined under pseudo-first-order conditions either from H₂S decays ([H₂S]₀ ≤ 4 × 10¹¹ molecule cm⁻³) in excess of hydrogen atoms, or from the kinetics of H-atom consumption ([H]₀ ≤ 2 × 10¹¹ molecule cm⁻³) monitored in excess of hydrogen sulfide. The concentrations of the excess reactants were varied between 0.18 and 6.64 × 10¹³ molecule cm⁻³ for H-atom, and between 0.85 and 44.7 × 10¹³ molecule cm⁻³ for [H₂S] (see

Table 1. Experimental conditions and results of the measurements of the rate constant of reaction (1).

T (K)	[Excess Reactant] a	k1 b	Reactor Surface c	Method d
220	6.51–24.2	0.24 ± 0.01	HW	H kinetics
235	4.80–28.8	0.26 ± 0.01	HW	H kinetics
250	3.66–28.4	0.31 ± 0.01	HW	H kinetics
270	1.60–44.7	0.39 ± 0.01	HW	H kinetics
285	0.85–27.8	0.49 ± 0.01	HW	H kinetics
295	0.66–4.37	0.60 ± 0.01	Q	H2S kinetics
305	1.09–19.7	0.59 ± 0.01	Q	H kinetics
325	1.25–20.4	0.77 ± 0.02	HW	H kinetics
330	0.46–6.64	0.88 ± 0.02	HW	H2S kinetics
360	0.62–5.58	1.07 ± 0.02	Q	H2S kinetics
410	0.45–4.60	1.58 ± 0.02	Q	H2S kinetics
475	0.57–5.87	2.61 ± 0.03	Q	H2S kinetics
575	0.43–4.46	4.61 ± 0.08	Q	H2S kinetics
720	0.33–3.31	9.96 ± 0.08	Q	H2S kinetics
950	0.18–2.61	20.6 ± 0.3	Q	H2S kinetics

^a Units of 10¹³ molecule cm⁻³. ^b units of 10⁻¹² cm³ molecule⁻¹s⁻¹; statistical 2σ uncertainty is given, total estimated uncertainty is 15%. ^c HW: halocarbon wax; Q: quartz. ^d k₁ derived from H₂S (H₂S kinetics) or H-atom (H kinetics) decays monitored in excess of H and H₂S, respectively.

). The linear flow velocity in the reactor was in the range of 1025–3400 cm s⁻¹.

Examples of H₂S decays observed at different excess concentrations of hydrogen atoms are shown in Figure 1. The consumption of the excess reactant, H atoms, along the reaction zone did not exceed a few percent (mainly due to the wall loss, k_w < 10 s⁻¹). In all cases, the average concentration of H was used in the calculations. The concentration of H₂S decays exponentially, [H₂S] = [H₂S]₀ × exp(−k₁^′ × t), where k₁^′ = k₁[H] is the pseudo-first-order rate constant of H₂S loss.

The pseudo-first-order rate constants, k₁^′, determined from the slopes of the straight lines like those in Figure 1, are shown in Figure 2, as a function of H-atom concentration.

One can note that the intercepts in Figure 2 are close to zero, which is consistent with the observed lack of H₂S consumption in the absence of hydrogen atoms in the reactor. Diffusion corrections were applied to all the measured values of k₁^′ in order to take into account the axial and radial gradient of H₂S concentration in the flow tube [25]. Corrections were generally less than 3%, and only at T = 950 K were they somewhat higher, reaching 7%. The slopes of the straight lines in Figure 2 provide the bimolecular rate constants at respective temperatures, which are summarized in Table 1.

In the second series of experiments, the kinetics of H-atom consumption in an excess of hydrogen sulfide was recorded. Figure 3 displays typical exponential decays of [H] with time, [H] = [H]₀ × exp(−k₁^′×t), where k₁^′ = k₁[H₂S] + k_w is the pseudo-first-order rate constant, with k_w representing the heterogeneous loss of H atoms.

Examples of the typical second-order plots observed at different temperatures are shown in Figure 4. The low intercept values of the plots in Figure 4 are in agreement with the wall loss rate of H atoms, k_w < 10 s⁻¹, measured in the absence of H₂S in the reactor. Diffusion corrections applied to the measured values of k₁^′ did not exceed 10%. Final values of k₁ determined in this series of experiments are presented in Table 1. The combined uncertainty on k₁ was estimated to be around 15% for both series of experiments by adding in quadrature statistical error (≤2%) and those on the measurements of the absolute concentration of H₂S (≈7%), (H) (≈10%), flows (3%), pressure (2%), and temperature (1%).

Reaction (1) produces SH radicals, and H-atom kinetics can be potentially impacted by the fast secondary reaction:

H + SH → S + H₂

(3)

The rate constant of reaction (3) is not well known. Measurements of k₃ available in the literature are scattered between 1.1 × 10⁻¹¹ and 4.15 × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹ at room temperature [4,8,10,26]. Although this secondary reaction is quite fast, its impact on the measurements of k₁ can be considered negligible due to the low initial concentrations of H atoms used ([H]₀ ≤ 2 × 10¹¹ molecule cm⁻³).

2.1.2. Comparison with Previous Data

Figure 5 shows the temperature-dependent data available for k₁. As noted in the Introduction section and as can be seen in Figure 5, the rate constant for reaction (1) is relatively well established.

The most reliable measurements of k₁ at room temperature [8,10,11,12] (not shown in Figure 5 for clarity) are in good agreement with each other. Bradley et al. [8] measured k₁ in a flow reactor using electron spin resonance for detection of hydrogen atoms: k_l = 8.3 × 10⁻¹³ cm³ molecule⁻¹ s⁻¹. The same value was reported for k₁ by Nicholas et al. [10] who monitored the concentrations of SH and S₂ intermediates upon decomposition of H₂S in a pulsed radio-frequency discharge and derived k₁ from computer simulation of SH and S₂ profiles. Husain and Slater [11] reported an absolute value of k_l = (8.6 ± 0.5) × 10⁻¹³ cm³ molecule⁻¹ s⁻¹, determined via the pulsed photolysis resonance fluorescence method. Finally, Clyne and Ono [12] measured k_l = (7.41 ± 0.39) × 10⁻¹³ cm³ molecule⁻¹ s⁻¹, employing resonance fluorescence method in a discharge flow system. It can be noted that the present value of k_l measured around room temperature, e.g., (6.0 ± 0.9) × 10⁻¹³ cm³ molecule⁻¹ s⁻¹ at T = 295 K, is somewhat lower than these previous measurements.

The first temperature-dependent measurement of the rate constant for reaction (1) was conducted by Mihelcic and Schindler [5], who used a discharge flow system combined with ESR detection of hydrogen atoms. The following Arrhenius equation was reported: k_l = (1.7 ± 0.1) × 10⁻¹¹ exp(−845 ± 25)/T] cm³ molecule⁻¹ s⁻¹ at T = 243–368 K. Kurylo et al. [6], using flash photolysis coupled with resonance fluorescence, carried out absolute measurements of k_l over a temperature range of 190–464 K, and reported k_l = (1.29 ± 0.15) × 10⁻¹¹ exp[ −(860 ± 30)/T] cm³ molecule⁻¹ s⁻¹. At high temperatures (T > 800 K), the rate constant of reaction (1) has been determined in three studies [9,13,14]. Pratt and Rogers [9] in their mass spectrometric study of the early stages of the exchange reaction in H₂S/D₂ mixture deduced values of k_l at T = 808–937 K, which are shown in Figure 5. Yoshimura et al. [13] and Woiki and Roth [14] studied reaction (1) behind reflected shock waves, applying atomic resonance absorption spectroscopy for the measurements of H-atom concentration, and reported k_l = 3.2 × 10⁻¹⁰ exp(−2491/T) at T = 1053–2237 K and k_l = 4.15 × 10⁻¹⁰ exp(−2890/T) cm³ molecule⁻¹ s⁻¹ at T = 1160–1722 K, respectively. As one can see in Figure 5, the results of these high temperature measurements are in good agreement. Finally, in the most recent study of the reaction (1) [15], k₁ was measured via the flash photolysis resonance fluorescence technique and found to be: k_l = 6.6 × 10⁻¹¹ exp(−1347/T) cm³ molecule⁻¹ s⁻¹ at T = 298–598 K.

The present measurements of k_l are in very good agreement with those of Kurylo et al. [6], Pratt and Rogers [9], and, in the range of experimental uncertainty, with the data from Peng et al. [15]. The k_l values measured by Mihelcic and Schindler [5] are a bit higher than others. Rommel and Schiff [7] suggested that the k_l values reported by Michelcic and Schindler [5] may have been overestimated. In fact, the values of k_l were derived from decays of H atoms under experimental conditions, where initial H₂S concentration was comparable to that of hydrogen atoms. In addition, secondary reaction (3), which should operate under such conditions, was not taken into account.

The present data for k_l obtained in a wide temperature range clearly show a well-pronounced curvature of the Arrhenius plot. The fit of the current data with the modified Arrhenius expression (the continuous black line in Figure 5) yields

k_l = 8.7 × 10⁻¹³ × (T/298)^2.87 × exp(−125/T) cm³ molecule⁻¹ s^−1.

This expression for k_l is recommended from the present study in the temperature range 220–950 K, with a conservative (independent of temperature) overall 2σ uncertainty of 15%. The black dashed lines in Figure 5 represent the deviations from this equation by a factor of 1.3, showing that practically all existing data (except at the highest temperatures) fall into this range.

It should be noted that the curvature of the Arrhenius plot is observed experimentally for the first time, although it was suggested in some previous studies. All previous experimental work was carried out over a limited temperature range, and resulted in “unmodified” Arrhenius expressions for k_l. Yoshimura et al. [13] based on their measurements of k_l at room and high temperatures (Figure 5) suggested a strong non-Arrhenius dependence of k_l on temperature, which was explained by a conventional transition-state theory combined with ab initio calculations. Peng et al. [15], combining their experimental data (T = 298–598 K) with those available in the literature, reported k_l = 5.8 × 10⁻¹⁷ × T^1.94 exp(−455/T) cm³ molecule⁻¹ s⁻¹ (blue dotted line in Figure 5). This expression reasonably (within 25%) describes the k_l data from the present work. The theoretical analysis carried out by the authors also supported the significant curvature of the Arrhenius plot. The experimentally observed non-Arrhenius temperature dependence of k_l was also reasonably reproduced by the recent quantum dynamics calculations of Qi et al. [2], concluding that the non-Arrhenius behavior is caused by the pronounced quantum tunneling. The calculations of Qi et al. [2] showed that both abstraction and exchange mechanisms are important for the H + H₂S reaction. Unfortunately, the available experimental data do not make it possible to define the contribution of these two mechanisms as a function of temperature.

2.2. Reaction H + C₂H₄S

2.2.1. Measurements of the Reaction Rate Constant

A similar experimental protocol described above for reaction (1) was also applied to measure the rate constant of the reaction of hydrogen atoms with thiirane. As in the previous case, the rate constant of reaction (2) was determined under pseudo-first order conditions by two methods: from kinetics of thiirane consumption ([C₂H₄S]₀ ≤ 3.6 × 10¹¹ molecule cm⁻³) in excess of hydrogen atoms and from H-atom decays ([H]₀ ≤ 2.1 × 10¹¹ molecule cm⁻³) recorded in excess of C₂H₄S. The concentrations of the corresponding excess reactants are shown in

Table 2. Experimental conditions and results of the measurements of the rate constant of reaction (2).

T (K)	[Excess Reactant] a	k2 b	Reactor Surface c	Method d
220	0.21–9.19	1.67 ± 0.04	HW	C2H4S kinetics
225	0.40–8.82	1.77 ± 0.03	HW	C2H4S kinetics
235	0.8–7.73	2.05 ± 0.04	HW	C2H4S kinetics
245	0.26–7.25	2.11 ± 0.03	HW	C2H4S kinetics
250	0.23–3.86	2.26 ± 0.06	HW	H kinetics
255	0.45–8.28	2.35 ± 0.04	HW	C2H4S kinetics
270	0.24–4.03	2.56 ± 0.07	HW	H kinetics
270	0.56–6.44	2.7 ± 0.04	HW	C2H4S kinetics
275	0.48–6.73	2.75 ± 0.07	HW	C2H4S kinetics
297	0.11–3.84	3.54 ± 0.04	Q	C2H4S kinetics
320	0.33–6.03	4.36 ± 0.04	HW	C2H4S kinetics
325	0.36–4.86	4.35 ± 0.08	HW	H kinetics
330	0.30–4.54	4.99 ± 0.06	HW	C2H4S kinetics
360	0.23–3.34	5.71 ± 0.06	Q	C2H4S kinetics
410	0.18–2.58	8.23 ± 0.07	Q	C2H4S kinetics
475	0.15–2.24	12.1 ± 0.1	Q	C2H4S kinetics
575	0.18–1.94	17.7 ± 0.1	Q	C2H4S kinetics
720	0.14–1.36	30.5 ± 0.2	Q	C2H4S kinetics
950	0.09–1.08	44.9 ± 0.1	Q	C2H4S kinetics

^a Units of 10¹³ molecule cm⁻³. ^b units of 10⁻¹² cm³ molecule⁻¹s⁻¹; statistical 2σ uncertainty is given; total estimated uncertainty is 15%. ^c HW: halocarbon wax; Q: quartz. ^d k₂ derived from C₂H₄S (C₂H₄S kinetics) or H-atom (H kinetics) decay monitored in excess of H and C₂H₄S, respectively.

. The flow velocity in the reactor was in the range (1045–3250) cm s⁻¹. Examples of second-order plots obtained from C₂H₄S and H-atom decays are shown in Figure 6 and Figure 7, respectively. The similarity of the results obtained with different initial concentrations of C₂H₄S (Figure 6, T = 220 K) and hydrogen atoms (Figure 7) indicates a minor influence of possible secondary chemistry on the measurements of k₂. The final values of k₂ determined at different temperatures from the slopes of the straight lines like those in Figure 6 and Figure 7 are shown in Table 2.

2.2.2. Comparison with Previous Data

The rate constant of the H + C₂H₄S reaction is displayed as a function of temperature in Figure 8. The present data on the temperature dependence of k₂ are best represented by the sum of two exponential functions (the continuous black line in Figure 8):

k₂ = 1.85×10⁻¹⁰ exp(−1410/T) + 4.17×10⁻¹² exp(−242/T) cm³ molecule⁻¹ s⁻¹

at T = 220–950 K (with an estimated conservative uncertainty of 15% at all temperatures).

To our knowledge, only two studies of the reaction are available in the literature. Yokota et al. [24] studied the reaction of thiirane with hydrogen atoms produced from the mercury photosensitization of H₂. The reaction rate constant was determined relative to that of the H-atom reaction with H₂S at three temperatures between 300 and 425 K: k₂ = (9.5 ± 1.2) × 10⁻¹¹ exp[−(980 ± 88)/T] cm³ molecule⁻¹ s⁻¹. The relative rate data were placed on an absolute basis with the values of k₁ reported by Kurylo et al. [6], which can be considered valid to date (see Figure 5). Lee et al. [20] carried out absolute measurements of k₂ using the flash photolysis–resonance fluorescence technique, and reported k₂ = (2.87 ± 0.12) × 10⁻¹¹ exp[−(945 ± 12)/T] cm³ molecule⁻¹ s⁻¹ over a temperature range from 223 to 423 K. The present data for k₂ clearly support the results of the relative rate measurements of Yokota et al. [24], being higher by a factor of 3–4 compared with the absolute measurements of Lee et al. [20] (Figure 8). The reason for such a large discrepancy is difficult to determine at this stage. Perhaps the point is in determining the absolute concentrations of thiirane, which (i) was photolyzed in the study of Lee at al. [20] to generate H atoms, and (ii) is known to decompose during storage.

In the study of Yokota et al. [24], C₂H₄, H₂S, and elemental sulfur were detected as reaction products in accordance with the formation of SH radical and C₂H₄ in the primary step, followed by the production of H₂S and S in the self-reaction of SH radicals:

SH + SH → S + H₂S

(4)

S + C₄H₄S → S₂ + C₂H₄

(5)

In this work, we also observed the formation of SH, S and S₂ under specific conditions (high concentrations of both reactants); however, quantitative measurements were quite difficult, and were not performed.

3. Materials and Methods

All experiments were performed in a conventional discharge fast-flow reactor coupled with a modulated molecular beam-sampling quadrupole mass spectrometer for the detection of the gas phase species [23]. Two different flow reactors (45 cm length and 2.4 cm i.d.) available in the laboratory were used. The low-temperature flow reactor, a Pyrex tube coated with halocarbon wax with a jacket for the circulation of thermostatically controlled ethanol (Figure 9), covered a temperature range between 220 and 330 K. The high-temperature flow reactor was employed over a temperature range of 295−950 K and consisted of an electrically heated uncoated Quartz tube with water-cooled attachments.

Hydrogen atoms were produced using two methods. The first one employed the microwave discharge of H₂/He mixtures. In the second method, H atoms were formed in the fast reaction of F atoms with H₂,

F + H₂ → H + HF

(6)

k₆ = 1.24 × 10⁻¹⁰ exp(−507/T) cm³ molecule⁻¹ s⁻¹ (T = 220–960 K) [27].

In this case, the fluorine atoms were generated in the microwave discharge of F₂/He mixtures and titrated with an excess of H₂ in the movable injector (Figure 9). The fraction of F₂ dissociated in the microwave discharge exceeded 95%. Ensuring that there was no molecular fluorine in the reactor was important in the presence of thiirane, since it was observed that these two stable compounds show high reactivity towards each other.

Low concentrations of hydrogen atoms were monitored using their chemical conversion to stable species HOBr (m/z = 96/98) upon addition of the NO₂/Br₂ mixture 5 cm upstream of the sampling cone of the mass spectrometer (Figure 9). In this configuration, H atoms are converted to HOBr in two successive rapid reactions (7) and (8):

H + NO₂ → OH + NO

(7)

k₇ = (1.47 ± 0.26) × 10⁻¹⁰ cm³ molecule⁻¹ s⁻¹ (T = 195–2000 K) [28],

OH + Br₂ → Br + HOBr

(8)

k₈ = 2.16 × 10⁻¹¹ exp(207/T) cm³ molecule⁻¹ s⁻¹ (T = 220–950 K) [29].

The concentrations of NO₂ and Br₂ were chosen so that the hydrogen atoms reacted primarily with NO₂ rather than with Br₂ in reaction (9):

H + Br₂ → Br + HBr

(9)

k₉ = 7.06 × 10⁻¹¹ (T/298)^0.88 exp(182/T) cm³ molecule⁻¹ s⁻¹ (T = 220–950 K) [30].

In experiments with high concentrations of hydrogen atoms (kinetics of H₂S, and C₂H₄S consumption in excess of H), they were detected at m/z = 80/82 (HBr⁺) after being transformed to HBr in reaction (9).

The absolute calibration of the mass spectrometer for HOBr was accomplished using reaction (8) in excess of Br₂, and relating the consumed fraction of Br₂ to the concentration of HOBr produced: [HOBr] = Δ[Br₂]. Absolute HBr concentrations were determined using two methods. In the first method, the absolute concentration of HBr was calculated from the flow rate of a manometrically prepared HBr/He mixture. The second method was the chemical transformation of the H atom into HBr in reaction (9), linking the consumed fraction of Br₂ and the concentration of HBr formed: [HBr] = Δ[Br₂]. The results of the two methods coincided within a few percent. The absolute concentrations of other stable species (Br₂, NO₂, F₂, H₂, H₂S and C₂H₄S) in the reactor were calculated from their flow rates, obtained from the measurements of the pressure drop of their monometrically prepared mixtures in He stored in calibrated volume flasks.

The purities of the gases used were as follows: He > 99.999% (Alphagaz); Br₂ > 99.99% (Aldrich); F₂, 5% in helium (Alphagaz); HBr > 99.8% (Praxair); H₂ > 99.998% (Alphagaz); NO₂ > 99% (Alphagaz); H₂S > 99.5% (Alphagaz); C₂H₄S (Merck), 98%.

4. Conclusions

In this work, we have investigated the kinetics of the reactions of H atoms with hydrogen sulfide and thiirane, using a discharge flow reactor combined with mass spectrometry. For the H + H₂S reaction, previously assumed on the basis of experimental and theoretical data, the strong curvature of the Arrhenius plot was confirmed via measurements of the reaction rate constant over an extended temperature range (220–950 K). Similar curved Arrhenius dependence was also observed for reaction of H atoms with C₂H₄S, which was studied at T = 220–950 K (and for the first time at T > 425 K). The reaction was found to be fast enough to be used as an alternative (free of H₂S) source of SH radicals (an important intermediate in combustion and atmospheric chemistry) in laboratory studies.